Method For Selecting Transmitting Points In A Communication System

ABSTRACT

The present invention provides a method for identifying a specific number of communicating points having relatively smallest accumulated path values from a plurality of transmitting points for a receiving point in a communication system. The method includes steps of: (a) defining a first coordination of each of the plurality of transmitting points and the receiving point on a complex plane; (b) transferring the first coordination of the receiving point to a second coordination thereof, in which the second coordination of the receiving point is near an origin of the complex plane; and (c) identifying the specific number of transmitting points having relatively smallest accumulated path values based on the second coordination of the receiving point.

FIELD OF THE INVENTION

The present invention relates to a receiver in a wireless communicationsystem, and more particularly to a method for selecting transmittingpoints from a plurality of candidates for a receiver in a wirelesscommunication system.

BACKGROUND OF THE INVENTION

In the field of wireless communication, the multi-input and multi-output(MIMO) system provides effective and promising solutions for achievinghigh data-rate with reliable transmission.

For example, in an MIMO communication system having M receiving antennafor receiving N transmitting signals from N transmitting antennas, foreach transmitted vector, the received signals can be shown as below:

$\begin{matrix}\begin{matrix}{y = \begin{bmatrix}y_{1} \\y_{2} \\\vdots \\y_{M}\end{bmatrix}} \\{= {{\begin{bmatrix}h_{1,1} & h_{1,2} & \cdots & h_{1,N} \\h_{2,1} & h_{2,2} & \cdots & h_{2,N} \\\vdots & \vdots & \ddots & \vdots \\h_{M,1} & h_{M,2} & \cdots & h_{M,N}\end{bmatrix}\begin{bmatrix}x_{1} \\x_{2} \\\vdots \\x_{N}\end{bmatrix}} +}} \\{{\begin{bmatrix}n_{1} \\n_{2} \\\vdots \\n_{M}\end{bmatrix}\begin{matrix}{M \geq N} \\{{\left. h_{i,j} \right.\sim i}.i.d.{{CN}\left( {0,1} \right)}} \\{{\left. n_{i} \right.\sim i}.i.d.{{CN}\left( {0,\sigma^{2}} \right)}}\end{matrix}}} \\{= {{Hx} + n}}\end{matrix} & {{Equation}\mspace{14mu} (1)}\end{matrix}$

Where y is the received vector having M elements, x is the vectorrepresenting the transmitted signals, H is the channel matrix of theMIMO communication system, and n is the noise vector. If there is nointerfering source that continuously affects the communication system,in other words, the noises existing in the communication system randomlyoccur. Therefore, the relationship between y and x are dependent uponthe channel matrix H and a disturbed term.

Please refer to FIG. 1, which schematics an algorism for sphere decodersknown to the art at a 2N-dimensional space. According to FIG. 1, a whitespot indicated as receiving point shows the location of a receivedsignal (an element of the vector y) in the 2N-dimensional space havingplural mesh points, each of which indicates the coordination of thetransmitting points (signals). An arrow in FIG. 1 shows a radius of a2N-dimensional hypersphere. The length of the arrow indicates apredetermined value. A number of calculations are performed bycalculating for the distance between each of the mesh point inside the2N-dimensional hypersphere and the receiving point to identify the meshpoint having the smallest distance to the receiving point.

An IEEE paper, “A Novel Approach for K-best MIMO Detection and its VLSIImplementation”, provides a method of searching for candidate nodes. Thesearching method set forth above can be split into N layers of searchingfor candidates on complex planes. Please refer to FIG. 2, whichschematics the method of searching for candidates known to the art. Themethod is doing search from a center of searching and starting from asearch inside the area of a circle centered at the center of searchingand having a radius of an initial value. If an effective transmitting(signal) point is found, the initial value of the radius is consideredas the path value of the founded effective transmitting (signal) point.Then the radius is increased step by step until the circle encompassesall the effective transmitting (signal) points on the complex plane.During the process, the value of the radius when the circle touches aneffective transmitting (signal) point is considered as the path value ofthe effective transmitting (signal) point. However, this method has somelarge defects: (1) For a particular circle, the amount of samplingpoints shall be sufficiently large so as to effectively contact all thenodes on the circle. For a particular value of the radius, each of thesampled points on the circle needs to be checked for the path valuethereof. Therefore, the total amount of calculation is huge. (2) Thecalculated path values are not the exact values, particularly when theradius is gradually enlarged. (3) If there are a large number ofeffective transmitting (signal) points to be sampled, either repeatedsampling or missing sampling might occur. So, the author of the paperadds a sub-module of redundancy remover to avoid such a dilemma.

Two searching algorithms, namely Schnorr-Eucher (SE) enumeration and theK-best method, are widely adopted particularly in the use of spheredecoders. However, the current methods for searching for the optimumtransmitting points on a complex plane cannot be both economical andreliable. The SE enumeration can achieve the same performance as themaximum-likelihood (ML) detector, which searches all possiblecombinations of transmitted symbols, with reduced complexity. Toovercome the abovementioned issues, the K-best method was introduced.The K-best method is proposed to avoid the mentioned issues by choosingan integer number k as the number of survival candidate nodes to becalculated for next layer of a searching tree, when the process ofsearching for the optimum transmitting points is simulated with thesearching tree model. However, the K-best method is a trade-off betweenthe performance and the computation loading, when determining the valueof k.

Whenever the number k is determined, only the k candidate nodes in eachlayer of the searching tree will be reserved for later calculation whilethe other candidate nodes will be given up. If the number k is small,the K-best method would save a large amount of calculations. But theproblem is: there is a good chance to give up the optimum candidates atthe early stage of the calculation.

SUMMARY OF THE INVENTION

To overcome the abovementioned drawback, the present invention providesa method for identifying a specific number of communicating pointshaving relatively smallest accumulated path values from a plurality oftransmitting points for a receiving point in a communication system. Themethod includes steps of: (a) defining a first coordination of each ofthe plurality of transmitting points and the receiving point on acomplex plane; (b) transferring the first coordination of the receivingpoint to a second coordination thereof, in which the second coordinationof the receiving point is near an origin of the complex plane; and (c)identifying the specific number of transmitting points having relativelysmallest accumulated path values based on the second coordination of thereceiving point.

Preferably, the step (c) further comprising the following sub-steps:(c1) providing a plurality of sequences, each of which includes pluralcandidates having accumulated path values respectively, and beingarranged in an increasing order according to the accumulated path valuesthereof; (c2) selecting one from the plurality of sequences based on thesecond coordination of the receiving point; (c3) choosing the specificnumber of candidates having the relatively smallest accumulated pathvalues from the selected sequence; (c4) identifying a secondcoordination of each of the specific number of candidates having therelatively smallest accumulated path values on the complex plane; and(c5) inversely transferring the second coordination of the each of thespecific number of candidates having the smallest accumulated pathvalues to the first coordination thereof. The plurality of sequences instep (a) are obtained by either calculating for the accumulated pathvalues of the candidates or looking up a table.

In accordance with another aspect of the present invention, a method forproducing a specific number of communicating candidates havingrelatively smallest accumulated path values is provided. The methodcomprises steps of: (a) providing a plurality of sequences, each ofwhich includes candidates having an accumulated path value respectively,and each of which follows an increasing order according to theaccumulated path values of the candidates; and (b) processing theplurality of sequences for identifying the specific number ofcommunicating candidates having relatively smallest accumulated pathvalues.

Preferably, the step (b) further comprises the following sub-steps: (b1)inputting at least a candidate according to the increasing order in eachof the plurality of sequences into a parallel processor, respectively;(b2) utilizing the parallel processor to identify at least a candidatehaving the respective relatively smallest accumulated path value fromthe inputted candidates; (b3) inputting a candidate subsequent to thecandidate identified in the step (b2) into the parallel processor; and(b4) repeating the steps (b1) to (b3) until the specific number ofcandidates having the relatively smallest accumulated path values areidentified.

Preferably, the parallel processor includes a plurality of inputentries. When a total number of the plurality of sequences exceeds atotal number of the input entries of the parallel processor, the methodfurther comprises steps of: (a1) arranging the plurality of sequencesinto a plurality of groups, wherein a total number of sequences in eachof the groups is one of equal to and less than the total number of theinput entries of the parallel processor; (a2) repeating the steps (b) to(d) for each of the groups until the specific number of the candidatesin the each groups having the relatively smallest accumulated pathvalues are identified; and (a3) turning the plurality of groups into theplurality of sequences, each of which includes the specific number ofcandidates having the relatively smallest accumulated path values in theeach group.

Preferably, the parallel processor includes j input entries, the j is aneven integer, and when the plurality of sequences are two sequences, thestep (b) comprises steps of: (bb1) inputting first k candidatesaccording to the increasing order in a first one of the two sequencesinto the odd-numbered input entries of the parallel processor, whereink=j/2; and (bb2) inputting first k candidates according to theincreasing order in a second one of the two sequences into theeven-numbered input entries of the parallel processor.

In accordance with a further aspect of the present invention, anoptimized K-best method in a multi-input multi-output (MIMO)communication system is provided. The method includes steps ofperforming a QR decomposition for a channel matrix of the MIMOcommunication system to obtain an R matrix having a plurality ofdiagonal elements and determining whether a K-best algorithm isperformed based on values of the diagonal elements. Preferably, themethod further comprising steps of determining an integer i based on adimension of the channel matrix and sequentially comparing therespective value of each of the i diagonal elements with a threshold, todetermine whether the K-best algorithm with a predetermined number ofcandidates is performed. For each of the i diagonal elements, thereexists a predetermined threshold.

Preferably, the i diagonal elements are the i diagonal elements countedfrom a bottom of the R matrix.

Preferably, the K-best algorithm is not performed for i layers of thecandidates, if all the compared values of the i diagonal elements do notexceed the corresponding thresholds.

Preferably, the integer i is obtained according to an cumulativepossibility function of the values of the diagonal elements.

Preferably, the method further comprises steps of allocating allcandidates available for the MIMO communication system into j sequences,when the K-best algorithm is not performed, wherein j is an integer,re-arranging the candidates of each of the j sequences in an increasingorder according to a relative path value of each of the candidates, andperforming a parallel calculation to identify a plurality of candidateshaving smallest relative path values from the re-arranged sequences.

Preferably, the relative path value is a distance on a complex plane.

Preferably, the step of re-arranging the candidates is implemented bylooking up a table, and the j is a smallest integer no less than asquare root of a total number of all the candidates available for theMIMO communication system.

The above objects and advantages of the present invention will be morereadily apparent to those ordinarily skilled in the art after readingthe details set forth in the descriptions and drawings that follow, inwhich:

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic diagram of an algorism for sphere decoders knownto the art at a 2N-dimensional space;

FIG. 2 is a schematic diagram illustrating a method of searching forcandidates known to the art;

FIG. 3 is illustrates a searching tree of 3 layers;

FIG. 4 a is a constellation diagram of 64-QAM;

FIG. 4 b shows a magnified diagram of the first quadrant of the dottedsquare area in FIG. 4 a;

FIG. 5 a illustrates the circuit layout of the CCPG provided by thepresent invention;

FIG. 5 b shows a parallel processor having 4 input entries;

FIG. 6 a is an exemplary distribution diagram illustrating theprobability of the square values of diagonal elements of the R matrixresulted from QR decompositions of the channel matrix of a wirelesscommunication system having 4 transmitting antennas and 4 receivingantennas;

FIG. 6 b is an exemplary distribution diagrams illustrating theprobability of the square values of diagonal elements of the R matrixresulted from QR decompositions of the channel matrix of a wirelesscommunication system having 8 transmitting antennas and 8 receivingantennas.

FIG. 7 is a schematic diagram illustrating a comparison of theestimation and the actual searching coverage on a constellation diagram;

FIG. 8 a is a constellation diagram illustrating the search constraintof the N^(th) layer with d_(c)=1.1 and r_(N,N)=1;

FIG. 8 b is a constellation diagram illustrating the search constraintof the N^(th) layer with d_(c)=1.1 and r_(N,N)=0.33;

FIG. 9 is a schematic diagram illustrating the cumulative distributionfunction shown as the Equation (3) for a 4-by-4 MIMO communicationchannel.

FIG. 10 is a schematic diagram illustrating the cumulative distributionfunction shown as the Equation (3) for an 8-by-8 MIMO communicationchannel.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT

The present invention will now be described more specifically withreference to the following embodiments. It is to be noted that thefollowing descriptions of preferred embodiments of this invention arepresented herein for the purposes of illustration and description only;it is not intended to be exhaustive or to be limited to the precise formdisclosed.

Please refer to FIG. 3, a schematic diagram showing a searching treehaving three layers, in which two branches exist in each node forexample. The structure of the searching tree shown in FIG. 3 simulatesan MIMO communication system having three receiving antennas and threetransmitting antennas, each of which is drawn from a signal setcontaining two signal points. Each node contains an accumulated pathvalue, and has two options for selecting the received signalsrespectively.

Starting from node 20, which contains an accumulated path value 200being zero in theory, there are two branches showing the path distances201 and 202 between the parent node 20 and the child nodes 21 and 22respectively. The node 21 contains an accumulated path value 210. Again,there are two branches showing the path distances 211 and 222 betweenthe parent node 21 and the child nodes 23 and 24 respectively. Node 23contains an accumulated path value 230 of the path from node 20 to node23 via node 21. Likewise, Node 27 contains an accumulated path value 270of the path from node 20 all the way to node 27 via nodes 21 and 23. Itcan be observed that there are eight nodes indicating all the eightpossible combinations of antennas versus signals in the MIMOcommunication system. Therefore, one may identify a node having thesmallest accumulated path value from one of the eight nodes at thebottom of the searching tree.

The Quadrature Amplitude Modulation (QAM) is often employed for carryingdata in wireless communication systems. QAM conveys data by changingsome aspect of a carrier signal, or the carrier wave, in response to adata signal. Similar to other methods of modulation, the group oftransmitted signals can be illustrated by a constellation diagram on acomplex plane. Please refer to FIG. 4 a, which schematics aconstellation diagram of a 64-QAM system. Totally 64 transmitting points0˜63 are placed at the locations whose coordination are odd integersnear the origin of the complex plane. According to FIG. 4 a, a receiveddata signal is located at a location x surrounded by points 41, 42, 49and 50 in the constellation diagram. The four transmitting points arethe ones having relatively smallest distances to the location x. Inaddition, a sequence, 49-50-41-42, can be identified in accordance withthe distance from the location x to the transmitting points. Nowconsider the dotted square area near the origin and surrounded by thetransmitting points 27, 28, 35 and 36. Transferring the coordination ofpoints 41, 42, 49 and 50 to the points 27, 28, 35 and 36 respectively, alocation y corresponding to the location x can be identified. A newsequence, 35-36-27-28, can be identified in accordance with the distancefrom the location y to the transmitting points. It is observed that therelations in terms of distance from the location x to all the nearbytransmitting points is remain unchanged after the mentioned spatialtransfer. It also can be easily observed that the coordination of thetransmitting points on the complex plane is symmetric both verticallyand horizontally. Once the special relations between a point in one ofthe four quadrants in the complex plane, say the first quadrant, andthose transmitting points have been identified, those of 3 points at themirrored locations in the other 3 quadrants can be derived by takingadvantage of the character of symmetry of the constellation diagram.

Please refer to FIG. 4 b, which shows a magnified diagram of the firstquadrant of the dotted square area in FIG. 4 a. The area shown in FIG. 4b is divided into 30 sections 401˜430. It is verified that, any locationin each of the sections 401˜430, the order in terms of distance from thelocation to the transmitting points 0˜63 is identical. For each of thesections 401˜430, a unique sequence that lists a number of transmittingpoints in accordance with an increasing order based on the distancethereof can be specified. Table 1 shows all the 30 sequences having 11elements according to one embodiment of the present invention. Withsimilar idea, one may construct different types of tables by dividingthe area in different ways, or choosing different number of elements inthe sequences.

TABLE 1 List of candidate sequences Section ID Candidate Sequence 40135→27→36→28→34→26→43→19→44→20→37 402 35→27→36→28→34→26→43→19→44→20→42403 35→27→36→28→34→26→43→19→44→42→20 40435→36→27→28→43→34→44→26→37→19→29 405 35→27→36→28→34→43→26→44→19→37→20406 35→27→36→28→34→26→43→44→19→20→37 40735→27→36→34→28→26→43→19→44→42→20 408 35→36→27→28→43→44→34→26→37→29→19409 35→36→27→28→43→44→34→37→26→29→19 41035→27→36→28→34→26→43→44→19→20→42 411 35→27→36→28→34→26→43→44→19→42→20412 35→27→36→28→34→43→26→44→19→37→42 41335→27→36→28→34→43→26→44→19→42→37 414 35→27→36→34→28→26→43→44→19→42→20415 35→27→36→34→28→26→43→44→42→19→20 41635→36→27→28→43→34→44→26→37→19→42 417 35→27→36→28→34→43→26→44→42→19→37418 35→27→36→34→28→43→26→44→42→19→37 41935→36→27→28→43→34→44→26→37→42→19 420 35→27→36→34→43→28→26→44→42→19→37421 35→36→27→28→43→34→44→26→42→37→19 42235→36→27→28→43→44→34→26→37→29→42 423 35→36→27→28→43→44→34→26→37→42→29424 35→36→27→28→43→44→34→37→26→29→42 42535→36→27→43→28→34→44→26→42→37→19 426 35→36→27→43→34→28→44→26→42→37→19427 35→36→27→28→43→44→34→37→26→42→29 42835→36→27→43→28→44→34→26→37→42→29 429 35→36→27→43→28→44→34→26→42→37→29430 35→36→27→43→28→44→34→37→26→42→29

Again, refer to FIGS. 4 a and 4 b. If one would like to identify 8transmitting point having the relatively smallest distances from thelocation x on the constellation diagram, he/she may identify the sectionwhere the y is located based on the coordination of y. For example, they is located at the section 423. According to Table 1, the first 8elements in the candidate sequence corresponding to the section 423 are:35, 36, 27, 28, 43, 44, 34 and 26, which identify the transmittingpoints having the relatively smallest distances to the location y. Sincethe spatial structure of the constellation diagram at different areasare similar to each other, the order in terms of distance from thelocation y to the identified transmitting points would be the same withthat of the location x to those transmitting points after a spatialtransfer to the identified transmitting points. For this example, thetransmitting points corresponding to 35, 36, 27, 28, 43, 44, 34 and 26are 49, 50, 41, 42, 57, 58, 48 and 40, respectively. Therefore, one mayobtain the 8 transmitting points having the smallest distances to thelocation x by looking up a table without calculation. If the table isnot available, the method of coordination or spatial transfer is stilluseful for the same purpose. Notably the distances on the constellationdiagram should be considered as path values between the receivingsignals and the transmitted signals in real practices.

There exist a variety of ways to identify the order in terms of thedistances between a particular location, says the x, to plural points,such as the transmitting points, located on the nodes of a complexplane. A useful method is to calculate for the value of each of thedistances and then compare the values to identify the order. Thosecandidate sequences listed in Table 1 can be obtained by means ofcalculating and comparing. Refer to FIG. 4 a, if all the candidate nodesare located on a line vertical to the X axis, says points 40˜44 forinstance, one may identify either an increasing or decreasing orderamong the distances from the location x to the points 40˜44 simply bycomparing the imaginary part of the path values thereof, since the realpart of the paths from the location x to the points 40˜44 are identical.Now consider all the candidate nodes are located on a line vertical tothe Y axis, says points 26, 34, 42, 50 and 58 for instance. Likewise,since the imaginary part of the paths from the location x to the points26, 34, 42, 50 and 58 are the same, either an increasing or decreasingorder among the distances from the location x to the points can beobtained by simply comparing the real part of the path values thereof.

FIG. 5 a illustrates the circuit layout of a complex plane pathcalculator module and candidate point generator (CCPG) 40 having a pathcalculator 41, a group of memories 42, a child node memory 43, a firstup-counter 44, a quadrant restore device 45, a weighting adjustmentdevice 46, a parent weight 47, a coordination transferor 48, a boundarychecker 49, and a second up-counter 50, according to one embodiment ofthe present invention. The CCPG 40 is capable for providing sequences,each of which includes candidates having an accumulated path valuerespectively, and each of which follows an increasing order according tothe accumulated path values of the candidates.

When the relative distance or path values of each of a plurality ofcandidates, such as transmitting points to be selected on theconstellation diagram, to a destination, say a receiving point, aredetermined, the method of parallel comparison is a useful tool foridentifying the candidate having the smallest path values to thedestination. Please refer to FIG. 5 b, which shows a parallel processor60 having four input entries. According to FIG. 5 b, the parallelprocessor 60 comprises registers 61˜64 disposed at the four inputentries, a first, a second and a third subtracters 65˜67, and a first, asecond and a third multiplexer 68˜70. Each of the subtracters 65˜67subtracts the values of the two candidates inputted therein to obtain avalue for judgment. The corresponding multiplexer receives the value forjudgment and selectively transmits the candidate having smaller value.

Now consider four candidates, namely A, B, C and D, are placed in theregisters 61˜64 for a comparison, it takes 3 steps for the parallelprocessor to complete the comparing and identify the candidate havingthe smallest value. Firstly, A is compared with B while C is comparedwith D. If A and C are the smaller ones, they will be transmitted by thefirst and the second multiplexer 68 and 69 respectively. Then A iscompared with C to identify the one who has the smallest value out ofthe four candidates. To identify the candidate having the secondsmallest value, assuming A has been identified as the one having thesmallest value, B is transmitted by the multiplexer 68 and be comparedwith C which has already been transmitted by the multiplexer 69.Therefore it takes only one more step for the parallel processor 60 toidentify the one having the second smallest value out of the fourcandidates. Then, the candidates having the third and the fourthsmallest values respectively can be identified by similar process. It isobserved that the one having the smallest value in N candidates can beidentified by parallel calculation with N−1 step, and a sequence of Nelements in an increasing order can be identified by means of parallelcalculation in (N−1)+(log₂N)*(N−1) steps. Compared with the traditionalbubble sort algorithm which needs N*(N−1)/2 steps of calculations toidentify a sequence of N elements in an increasing order, the method ofparallel calculation saves a lot of calculations particularly when N isa large integer. The main advantage of the method of parallel comparisonis that it avoids some unnecessary steps of comparison based on knownresults.

The present invention takes advantages of the method of parallelcalculation in a variety of novel applications. According to a preferredembodiment, the present invention provides a method for identifying aspecific number of candidates having the relatively smallest values,such as accumulate path values or distances, from a plurality ofcandidates. The plurality of candidates is firstly divided into a numberof groups, where the number is the same with the number of input entriesof a parallel processor to be used. In this example, since the parallelprocessor 60 illustrated in FIG. 5 b has four input entries, theplurality of candidates are arranged into four groups, say A, B, C andD. The purpose for this embodiment is to select the specific number, say4 for example, from a big number of candidates, for example, 64candidates. The 64 candidates are evenly divided into the 4 groups, soeach of the groups A, B, C and D comprises 16 candidates.

Taking group A for instance, it contains candidates A1˜A16. Again, groupA can be evenly divided into four subgroups, namely Aa, Ab, Ac and Ad,each of which comprises four candidates. For example, Aa comprisesA1˜A4, Ab does A5˜A8, Ac does A9˜A12, and Ad does A13˜A16. For eachsubgroup, a sequence in increasing order based on the values of thecandidates can be identified by using the parallel processor 60. Then,one may arrange the four sequences following increasing order accordingto the value of the candidates thereof at each of the input entries ofthe parallel processor 60 so that the candidate having the smallestvalue of each sequence is entered the parallel processor 60. Forexample, the one from the subgroup Aa, Ab, Ac and Ad are at the first,the second, the third, and the fourth input entries 61˜64 respectively.After a parallel comparison implemented by the parallel processor 60,the candidate having the smallest value is identified, for example thecandidate A1 which is from the subgroup Aa. Then, the candidate havingthe second smallest value in the subgroup Aa is entered the first inputentry 61 of the parallel processor 60. The newly entered candidate iscompared with the one already at the second input entry 62 in terms ofthe value. The smaller one is then compared with the candidate thatalready registered at the multiplexer 69. After comparison, thecandidate having the second smallest value is identified and transmittedfrom the multiplexer 70. Likewise, the candidates having the third andfourth smallest values of group A therein can be identified by the sameprocess. Now, a sequence of four candidates having the smallest, thesecond smallest, the third smallest and the fourth smallest values ofgroup A therein and listed in increase order is therefore identified.

Likewise, the sequences of four candidates having the smallest, thesecond smallest, the third smallest and the fourth smallest values ingroups B, C and D can be identified by the similar process. Repeatingthe same process by placing each of the sequences having the smallest,the second smallest, the third smallest and the fourth smallest valuesin groups A˜D toward the input entries 61˜64 of the parallel processor60 respectively, and replacing the identified candidate whenever it isidentified with the next candidate from the same sequence that theidentified candidate is from, eventually the four candidates having thesmallest values can be identified.

An alternative way for the abovementioned embodiment is to obtain asequence having all the candidates following an increasing orderaccording to their values for each of the groups A, B, C, and D. So, thecorresponding sequences for groups A˜D each comprises 16 candidates. Forthis particular example, a larger number of candidates having thesmallest values, such as 7 but no larger than 16, can be identified byimplementing the same procedure set for above.

According to another preferred embodiment, the present inventionprovides a method for identifying a specific number of candidates havingthe relatively smallest values, such as accumulated path values ordistances, from two groups of candidates. Firstly, a sequence followingan increasing order according to the values of the candidates for eachof the two groups is obtained either by calculating, such as using theCCPG 40 illustrated in FIG. 5 a, or by looking up tables if applicable.For instance, the two sequences, namely sequence A and sequence B,include candidates A1˜A16 and B1˜B16 respectively. Notably, thecandidates A1˜A16 and B1˜B16 respectively in sequences A and B arelisted in an increasing order according to the values of the candidates.

A parallel processor usually has totally even number of input entries,say L for example. If each of the input entries is identified with aninteger and all the integers used for identifying the input entries arein an integral sequence, there are L/2 input entries having evenidentification numbers while L/2 having odd identification numbers. Thefirst L/2 candidates in one of the sequences, sequence A for instance,are arranged to the odd-numbered input entries and the first L/2candidates in the other sequence, sequence B for this example, to theeven-numbered input entries. Since there are four input entries 61˜64 inthe parallel processor 60, there are two input entries 61 and 63 of oddinput entry numbers while the other two input entries 62 and 64 of eveninput entry numbers. The first two candidates in the sequence A, A1 andA2, is placed at the odd-numbered input entries 61 and 63, while thefirst two candidates in the sequence B, B1 and B2, at the even-numberedinput entries 62 and 64, respectively. After implementing a first roundof parallel calculations by the parallel processor 60, the candidatehaving the smallest value of the two groups is identified. For example,the value of A1 is smaller than that of B1 and the value of B2 issmaller than that of A2, so A1 is transmitted by the multiplexer 68 andB2 in transmitted by the multiplex 69. Since the value of A1 is smallerthan that of B2, A1 is then transmitted by the multiplexer 70 and isidentified as the one having the smallest value in the two groups ofcandidates. Afterwards, the input entry 61 is filled in with A3, for A3is from the same sequence of A1. The second round of calculation needsonly two steps, for the result of the comparison between A2 and B2 isknown, and the candidate having the second smallest value in the twogroups is then identified.

Again, the next candidate to be filed into the input entry to replacethe identified candidate having the second smallest value is selectedfrom the same sequence thereof. Likewise, the process is repeated untilthe specific number of candidates having the relatively smallest valuesin the two groups are identified. The method set for above can also beemployed for combining the two sequences A and B into one sequencefollowing an increasing order according to the values of the candidatesthereof, when the process is continued until the order of all thecandidates A1˜A16 an B1˜B16 in terms of the value has been identified.

To save the calculation resources when adopting a search tree analysiswherein each parent node is connected to a large number of child nodes,one method is to choose a specific number of nodes having relativelysmaller accumulated path values during the calculation at each layer ofthe searching tree. The method is the so-called K-best method. Forexample, say there are 15 transmitting antennas and 20 receivingantennas in an MIMO communication system. A 16-QAM signal is transmittedat each transmit antenna, a K value which equals to 8 is chosen as thespecific number. Since there are 15 transmitting antennas and 20receiving antennas in the MIMO communication system in the particularexample, the searching tree for modeling the system should have 15layers, wherein each of the parent nodes is connected to 16 child nodes.During the calculation process at the first layer, 8 nodes having therelatively smallest accumulated path values are identified and theaccumulated path values at the child nodes thereof are calculated.Accordingly, the other 8 nodes having larger accumulated path valueswill be given up for subsequent calculations. Then during thecalculation process at the second layer, since there are 128 child nodesat the layer, only 8 nodes will be reserved while the other 120 oneswill be given up. The K-best method helps save a lot of calculations forthe decoding process.

One concern for the K-best method is whether it is appropriate to giveup the many nodes of the searching tree at some early stages of thecalculation process. When a certain number of the path values exit insome low layers of the searching tree, it might be not a good idea togive up any number of nodes too early. Otherwise, the node actuallyhaving the smallest accumulated path value would never be found.Therefore, it will still need to choose a large K value for adopting theK-best method. Again, when the chosen value of K is larger, the overallloading for calculation and the power consuming become larger too.

Some methods have been proposed to resolve the mentioned issue. Eachmethod is described as below:

Method 1: Performing a singular value decomposition to the channelmatrix of the communication system, and determining the K value based onthe condition values calculated by the singular value decompositionprocess. The purpose thereof is to choose a larger K value when thecondition values of the channel matrix is large, so as to reserve themaximum-likelihood solutions. However, such a method consumes a hugeamount of calculation while doing the singular value decomposition, andends up with a surge in power consuming and a lower overall throughput.

Method 2: Directly choosing a large K value, to assure the proper nodesis reserved. The price for this method is high amount of calculation aswell as high power consumption.

Method 3: Performing the maximum-likelihood calculation at the first fewlayers of the searching tree without exception, and adopting the K-bestmethod afterwards. However, there has been no theoretical analysis todetermine how many layers that the maximum-likelihood calculation isnecessary, according to the published articles, only comparisons amongthe relative efficacies of maximum-likelihood calculation at differnumbers of layers by means of either complexity analysis or computersimulation can be found. From a hardware application point of view, themore layers of maximum-likelihood searching induces not only largeamount of calculation as well as high power consumption but also a hugerequirement of memory space for storing the information of each of thepossible candidates.

Method 4: Performing the maximum-likelihood calculation at the first fewlayers of the searching tree without exception but adopting a smaller Kvalue for the K-best method afterwards to reduce the overall amount ofcalculation. The methods 3 and 4 are similar in theory.

According to one embodiment of the present invention, an optimumresolution to the mentioned issue is to maintain a maximum-likelihoodcalculation for the first few layers of the searching tree, based on ananalysis to the channel matrix, and adopt the K-best method afterwards.Additionally, this embodiment suggests a parallel calculation process tobe utilized for reducing the overall amount of calculation when themaximum-likelihood searching is needed.

It is known to the skilled person in this art that the values of thediagonal elements of the R matrix resulting from a QR decomposition tothe channel matrix of a communication system may reflect the conditionof the communication system at times. Please refer to FIGS. 6 a and 6 b,which are exemplary distribution diagrams illustrating the probabilityof the square values of diagonal elements of the R matrix resulted fromordering QR decompositions to the channel matrices of wirelesscommunication systems, each of which has 4 transmitting antennas and 4receiving antennas and 8 transmitting antennas and 8 receiving antennas,respectively. It is observed from FIGS. 6 a and 6 b that, for thediagonal elements corresponding to the last two layers, there areconsiderably high probabilities the values of the diagonal elements arevery small. Under the condition the values thereof are small, the numberof effective signal points would be very large when the values issubstituted back into the equations. Consequently, the scope ofeffective signal points might cover all the points available on thecomplex plane. When the K-method is adopted, there is a good opportunitythat the real solution is given up for only K items at each layer ofsearching is reserved for subsequent calculation, and end up withdecreased efficacy of the system. Based on the exemplary probabilitydistribution functions corresponding to the two exemplary distributiondiagrams, FIGS. 6 a and 6 b, the abovementioned effect willsignificantly decrease after entering into the searching at the thirdlayer. Therefore, taking advantage of such a character, the presentinvention provides an assessor and the method thereof to determinewhether to start a maximum-likelihood searching. Utilizing the assessorprovides a judgment mechanism, which prevents discarding the realsolution at the early stages of the searching process. Notably, themaximum-likelihood searching is not applicable to all conditions ofcommunication channels. Nevertheless, the method provided by the presentinvention can significantly reduce unnecessary efforts to achieve thepurpose of low power consuming.

Since the maximum-likelihood searching is sometimes necessary, onepreferred embodiment also make use of the CCPG 40 and the parallelprocessor 60, illustrated in FIGS. 4 a and 4 b respectively, toimplement the process at a high efficiency and reduce a great deal ofhardware cost and power consumption.

Based on the concepts set forth above and observations as well asanalysis over massive experiment data, the present invention provides ajudging method for whether to employ the maximum-likelihood searching.In brief, whether the method of maximum-likelihood searching is to beemployed depends on a calculation result of the following equations:

$\begin{matrix}\begin{matrix}{\frac{T_{r}^{2}D_{K,\min}^{2}}{E\left\{ \left( d_{c} \right)^{2} \right\}} = 1} & {\left( d_{c} \right)^{2} = {{y - {Hx}_{ZF}}}^{2}}\end{matrix} & {{Equation}\mspace{14mu} (2)}\end{matrix}$

Where T_(r) is the threshold value to be found;

D²K,min is square value of the equivalent radius for collecting Kpoints;

E{(d_(c))²} is the estimation of square value of the distance betweenthe receiving point and the zero-forcing solution point.

That is to say, refer to FIG. 7, the last two diagonal elements in the rmatrix, r_(N,N) and r_(N−1,N−1) are effective in a circle of anequivalent radius which is smaller than the distance between the actualpoint and the zero-forcing solution point. Under such a condition, someof the good candidates might be discarded when reserving K points forsubsequent searching. Therefore, the maximum-likelihood searching issuggested to be employed at the first and the second layers of thesearching tree. Then, K nodes having the relatively smallest accumulatedpath values are chosen to be continued on the searching process.Therefore, the process returns to the traditional K best algorithm.

The present invention also provide a further embodiment to deal with thecomplexity of conventional K-best method which doing the searching for anumber of transmitting points having relatively smallest accumulatedpath values in an MIMO wireless communication system. Instead ofchoosing a sufficiently large K to achieve a performance near that ofthe maximum likelihood method. The embodiment reserves all candidatesfor performing the maximum likelihood search in the first few layers ofthe searching tree when dealing with poor channel conditions of thecommunication system, and the K-best method is adopted for the remaininglayers of searching.

Given matrices Q_(o) and R_(o) denoting the QR decomposition of aordered channel matrix H_(o), the cumulative distribution function ofthe square value of the diagonal entries of R_(o) is shown as below.Noted the square value of the diagonal entries of R_(o) is denoted as r_(—) _(o) _(—) _(i,i) ², where i indicates the number of row where thedemoted diagonal entry is located.

$\begin{matrix}{{{{for}\mspace{14mu} i} = 1}{{F_{r_{o,i,i}^{2}}(r)} = {\int_{0}^{r}{{{\frac{N!}{{\left( {N - 1} \right)!}{\left( {M - 1} \right)!}}\left\lbrack {\sum\limits_{k = 0}^{M - 1}{\frac{x^{k}}{k!}^{- x}}} \right\rbrack}^{N - 1} \cdot x^{M - 1}}^{- x}{x}}}}{{{for}\mspace{14mu} 2} \leq i \leq N}{{F_{r_{o,i,i}^{2}}(r)} = {C_{ii}{\int_{0}^{1}{\int_{0}^{r/3}\begin{matrix}{\left\lbrack {1 - {\sum\limits_{k = 0}^{M - 1}{\frac{x^{k}}{k!}^{- x}}}} \right\rbrack^{i - 1}\left\lbrack {\sum\limits_{k = 0}^{M - 1}{\frac{x^{k}}{k!}^{- x}}} \right\rbrack}^{N - i} \\{x^{M - 1}{^{- x}(s)}^{M - i}\left( {1 - s} \right)^{i - 2}{x}{s}}\end{matrix}}}}}{where}{C_{ii} = {\frac{N!}{{\left( {N - i} \right)!}{\left( {M - i} \right)!}{\left( {i - 1} \right)!}{\left( {i - 2} \right)!}}.}}} & {{Equation}\mspace{14mu} (3)}\end{matrix}$

To reduce computational complexity, the embodiment proposes to maintainthe maximum likelihood searching at the first few layers of searchingwhile conducting the K-best method afterwards, if there is any r _(—)_(o) _(—) _(i,i) whose values is less than a given threshold T_(r).Please refer to FIGS. 8 a and 8 b, which illustrates the relationbetween the value of the diagonal entries r _(—) _(o) _(—) _(i,i) andthe searching regions. A received signal data is located at a location xon each of the constellation diagrams as shown in FIGS. 8 a and 8 b. Thecircles indicate the searching regions and the black spots are thecandidate transmitting points identified by of the searching. The valuesof r _(—) _(o) _(—) _(i,i) equal to 1 and 0.33 for the exampleillustrated by FIGS. 8 a and 8 b, respectively. It appears that thesearching region is larger when the value of r _(—) _(o) _(—) _(i,i) issmaller, particularly when the value of r _(—) _(o) _(—) _(i,i) is lessor equal to 1. Therefore, when the absolute value of r _(—) _(o) _(—)_(i,i) is very close to 0, the number of identified candidates will bevery large. If only a limited number of candidates, or transmittingpoints, are reserved for the sequent searching steps, there will be agood opportunity to drop the optimal candidates at the early stage ofthe searching process.

Based on the results derived from the Equation (3), one maysystematically determine the number of layers for maintaining themaximum likelihood searching. FIG. 9 schematics the cumulativedistribution function shown as the Equation (3) for a 4-by-4 MIMOcommunication channel. The probability for the value of which is lessthan 1 in the 4^(th) layer is significantly larger than that in theother layers. Hence, a preferred embodiment is to perform the maximumlikelihood search at the 4^(th) layer only. FIG. 10 schematics thecumulative distribution function shown as the Equation (3) for an 8-by-8MIMO communication channel. In such an example, the probability for thevalues of r _(—) _(o) _(—) _(i,i) less than 1 in the 7^(th) and the8^(th) layers are significantly larger than those in the other layers.Therefore, a preferred embodiment is to perform the maximum likelihoodsearch at the 7^(th) and the 8^(th) layers.

Next, we discuss how to determine the threshold T_(r).

T _(r) D≧E[(d′)²]; where D=Min(Dk,D ₁₁)   Equation (4)

Where Dk and D11 denote the distances from the Kth and 11^(th) nearesttransmitting points to the signal point x on the constellation diagram,respectively.

From Equation (4), when the k nearest constellation nodes do not coverall the candidates inside the circle having a radius of the valueE[(d′)²]^(1/2), a maximum likelihood method can be activated to retainall valid nodes. However, this will incur increased complexity becausethe probability of performing the maximum likelihood method increases.The threshold T_(r) thus acts as a trade-off parameter betweencomplexity and performance.

When applying Equation (4) as a criterion to the (N−1)^(th) layer andbelow, the obtained threshold is sure to be smaller than that of theN^(th) layer because the distance contributed by the N^(th) layer is apositive value. Thus, one may apply the threshold of the N^(th) layer toother layers. Furthermore, a table covering most of the possiblecombinations of the numbers of receiving antenna and transmittingantenna in an MIMO wireless communication system can be worked out basedon the cumulative possibility function provided from Equation (3) andthose diagrams such as FIGS. 9 and 10 based on the accumulativepossibility function, to help determining the number of layers formaintaining the maximum likelihood searching.

While the invention has been described in terms of what is presentlyconsidered to be the most practical and preferred embodiments, it is tobe understood that the invention needs not be limited to the disclosedembodiments. On the contrary, it is intended to cover variousmodifications and similar arrangements included within the spirit andscope of the appended claims that are to be accorded with the broadestinterpretation so as to encompass all such modifications and similarstructures.

1. A method for identifying a specific number of communicating pointshaving relatively smallest accumulated path values from a plurality oftransmitting points for a receiving point in a communication system, themethod comprising steps of: (a) defining a first coordination of each ofthe plurality of transmitting points and the receiving point on acomplex plane; (b) transferring the first coordination of the receivingpoint to a second coordination thereof, wherein the second coordinationof the receiving point is near an origin of the complex plane; and (c)identifying the specific number of transmitting points having relativelysmallest accumulated path values based on the second coordination of thereceiving point.
 2. A method as claimed in claim 1, wherein the step (c)further comprising the following sub-steps: (c1) providing a pluralityof sequences, each of which includes plural candidates havingaccumulated path values respectively, and being arranged in anincreasing order according to the accumulated path values thereof; (c2)selecting one from the plurality of sequences based on the secondcoordination of the receiving point; (c3) choosing the specific numberof candidates having the relatively smallest accumulated path valuesfrom the selected sequence; (c4) identifying a second coordination ofeach of the specific number of candidates having the relatively smallestaccumulated path values on the complex plane; and (c5) inverselytransferring the second coordination of the each of the specific numberof candidates having the smallest accumulated path values to the firstcoordination thereof.
 3. A method as claimed in claim 1, wherein theplurality of sequences in step (a) are obtained by one of calculatingfor the accumulated path values of the candidates and looking up atable.
 4. A method for producing a specific number of communicatingcandidates having relatively smallest accumulated path values, themethod comprising steps of: (a) providing a plurality of sequences, eachof which includes candidates having an accumulated path valuerespectively, and each of which follows an increasing order according tothe accumulated path values of the candidates; and (b) processing theplurality of sequences for identifying the specific number ofcommunicating candidates having relatively smallest accumulated pathvalues.
 5. A method as claimed in claim 4, wherein the step (b) furthercomprising the following sub-steps: (b1) inputting at least a candidateaccording to the increasing order in each of the plurality of sequencesinto a parallel processor, respectively; (b2) utilizing the parallelprocessor to identify at least a candidate having the respectiverelatively smallest accumulated path value from the inputted candidates;(b3) inputting a candidate subsequent to the candidate identified in thestep (b2) into the parallel processor; and (b4) repeating the steps (b1)to (b3) until the specific number of candidates having the relativelysmallest accumulated path values are identified.
 6. A method as claimedin claim 4, wherein the plurality of sequences in the step (a) areobtained by looking up a table.
 7. A method as claimed in claim 4,wherein the plurality of sequences in the step (a) are obtained bycalculating the accumulated path values of the candidates.
 8. A methodas claimed in claim 5, wherein the parallel processor includes aplurality of input entries, and when a total number of the plurality ofsequences exceeds a total number of the input entries of the parallelprocessor, the method further comprises steps of: (a1) arranging theplurality of sequences into a plurality of groups, wherein a totalnumber of sequences in each of the groups is one of equal to and lessthan the total number of the input entries of the parallel processor;(a2) repeating the steps (b) to (d) for each of the groups until thespecific number of the candidates in the each groups having therelatively smallest accumulated path values are identified; and (a3)turning the plurality of groups into the plurality of sequences, each ofwhich includes the specific number of candidates having the relativelysmallest accumulated path values in the each group.
 9. A method asclaimed in claim 5, wherein the parallel processor includes j inputentries, the j is an even integer, and when the plurality of sequencesare two sequences, the step (b) comprises steps of: (bb1) inputtingfirst k candidates according to the increasing order in a first one ofthe two sequences into the odd-numbered input entries of the parallelprocessor, wherein k=j/2; and (bb2) inputting first k candidatesaccording to the increasing order in a second one of the two sequencesinto the even-numbered input entries of the parallel processor.
 10. Anoptimized K-best method in a multi-input multi-output (MIMO)communication system, comprising steps of: performing a QR decompositionfor a channel matrix of the MIMO communication system to obtain an Rmatrix having a plurality of diagonal elements; and determining whethera K-best algorithm is performed based on values of the diagonalelements.
 11. A method as claimed in claim 10, further comprising stepsof: determining an integer i based on a dimension of the channel matrix;and sequentially comparing the respective value of each of the idiagonal elements with a threshold, to determine whether the K-bestalgorithm with a predetermined number of candidates is performed.
 12. Amethod as claimed in claim 11, wherein the i diagonal elements are the idiagonal elements counted from a bottom of the R matrix.
 13. A method asclaimed in claim 11, wherein the K-best algorithm is not performed for ilayers of the candidates, if all the compared values of the i diagonalelements do not exceed their corresponding thresholds.
 14. A method asclaimed in claim 11, wherein the integer i is obtained according to acumulative possibility function of the values of the diagonal elements.15. A method as claimed in claim 10, further comprising steps of:allocating all candidates available for the MIMO communication systeminto j sequences, when the K-best algorithm is not performed, wherein jis an integer; re-arranging the candidates of each of the j sequences inan increasing order according to a relative path value of each of thecandidates; and performing a parallel calculation to identify aplurality of candidates having smallest relative path values from there-arranged sequences.
 16. A method as claimed in claim 15, wherein therelative path value is a distance on a complex plane.
 17. A method asclaimed in claim 15, wherein the relative path value is a real part of adistance on a complex plane.
 18. A method as claimed in claim 15,wherein the relative path value is an imaginary part of a distance on acomplex plane.
 19. A method as claimed in claim 16, wherein the step ofre-arranging the candidates is implemented by looking up a table.
 20. Amethod as claimed in claim 16, wherein the j is a smallest integer noless than a square root of a total number of all the candidatesavailable for the MIMO communication system.